Simplify the following expression: $ a = \dfrac{-3}{2} - \dfrac{2q + 4}{9q + 8} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9q + 8}{9q + 8}$ $ \dfrac{-3}{2} \times \dfrac{9q + 8}{9q + 8} = \dfrac{-27q - 24}{18q + 16} $ Multiply the second expression by $\dfrac{2}{2}$ $ \dfrac{2q + 4}{9q + 8} \times \dfrac{2}{2} = \dfrac{4q + 8}{18q + 16} $ Therefore $ a = \dfrac{-27q - 24}{18q + 16} - \dfrac{4q + 8}{18q + 16} $ Now the expressions have the same denominator we can simply subtract the numerators: $a = \dfrac{-27q - 24 - (4q + 8) }{18q + 16} $ Distribute the negative sign: $a = \dfrac{-27q - 24 - 4q - 8}{18q + 16}$ $a = \dfrac{-31q - 32}{18q + 16}$